On 05/11/95 at 17:57:14 mreid@ptc.com said:

jerry asks about P-symmetric positions. coincidentally, i happened
to investigate these a few weeks back, and here's what i found:
(i calculated by hand, so i'd be grateful for any confirmation.)

there are 128 P-symmetric positions, 4 of which are M-symmetric.

I can confirm your count. These positions are called X class positions
in Dan's taxonomy. That is, there are 124 positions Y unique up to
M-conjugancy for which Symm(Y)=X1 or Symm(Y)=X2 or Symm(Y)=X3, where
X1, X2, and X3 are the three conjugate subgroups of M in Dan's
taxonomy of subgroups which contain sixteen elements. Hence, we
describe the 124 positions as being class X positions. The 4
M-symmetric positions are also X-symmetric, but we don't count them
as class X.

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Robert G. Bryan (Jerry Bryan)                        (304) 293-5192
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